Bombard, B.

Boswell, C.J.

Goetz, J.A.

Lipschultz, B.

Terry, J.L.

DSpace@MIT

Observations of Cold, High Density Plasma inthe Private Flux Region of the Alcator C-ModDivertorC. J. Boswell, J. L. Terry, B. LaBombard, B. Lipschultz, andJ. A. GoetzM. I. T. Plasma Science and Fusion Center175 Albany Street, Cambridge, MA 02139 USAAbstractSignificant plasma density has been observed in the private flux zone of the AlcatorC-Mod tokamak. The behavior of the Dγ emission profiles is consistent with thesource of the plasma being due to an ~E× ~B drift generated by a poloidal temperaturegradient. The plasma flux due to this drift is derived and evaluated. A plasma fluxinto the private flux zone is inferred by measurements of volumetric recombinationusing a tangentially viewing CCD camera and several spectroscopic views observingthe high n-lines of the Do Balmer series. For the case of an attached divertor theinferred plasma flux to the PFZ has a linear scaling with respect to plasma pressure,as is expected from the temperature-gradient-induced, ~E × ~B drift.Key words: ExB drift, Alcator C-Mod, Divertor Spectroscopy, RecombinationPACS:1 IntroductionAlcator C-Mod is a high magnetic field, high density, compact tokamak, witha parallel heat flux to the divertor as high as 600 MWm−2.[1] The tokamakis operated in a single lower null magnetic configuration. The data presentedhere are from a series of experiments where argon and krypton were puffedinto the vacuum vessel early in the discharge. In all of these shots the densitywas raised during the discharge (typically n¯e = 1.0 → 2.5 × 1020 m−3). Theinner leg of the divertor for these shots is nearly always detached. The outerdivertor leg progresses through attached and then increasingly detached con-ditions (the radiation front moves from the divertor plate to the x-point). Theassessment of detached conditions is made by a comparison of pressures fromPreprint submitted to Journal of Nuclear Materials 5 July 20000.40 0.50 0.60 0.70 0.80R [m]-0.60-0.55-0.50-0.45-0.40-0.35-0.30Z [m]Fig. 1. The triangles are the locations of the flush-mounted probes and the straightlines are the chordal views of the visible spectrometer.a reciprocating probe scanning the main plasma scrape-off-layer (SOL) andLangmuir probes which are flush-mounted in the divertor plates.[2]Deuterium line radiation, specifically Dγ (n = 5 → 2 transition), has beenobserved to be emitting from the private flux zone (PFZ) during divertedoperation. The PFZ is the region below the x-point and bounded by the sepa-ratrix and the vacuum vessel in Fig. (2). Typically, strong Dγ emission in thedivertor region has been associated with detached divertor operation. Dγ emis-sion along with other spectroscopic data are used to measure the volumetricrecombination.[3–7]2 DiagnosticsThree diagnostics were used to obtain the information used in the analysisof the PFZ plasma. The first diagnostic is a set of flush-mounted Langmuirprobes on the outer and inner divertor plates.[2] The Langmuir probes areused to determine plasma density and temperature in both the common fluxzone (CFZ) and the PFZ at the divertor plates. The locations of the probesare shown in Fig. (1) by green triangles.The second diagnostic used is a CCD camera filtered for Dγ emission and view-ing the entire divertor tangentially. Calibrated brightness images recorded bythe camera are inverted using tomography and the assumption of the toroidalsymmetry of Dγ emission to yield 2D emission profiles. The profiles are foundto be in agreement with the chord-integrated Dγ measurements made by thevisible spectrometer.The third diagnostic is a visible spectrometer with multiple views of thedivertor. The chordal views used of the visible spectrometer are shown inFig. (1). The spectrometer is used to measure the temperature and density2of the plasma in the regions of brightest emission. The density is determinedby measuring the Stark broadening of the p = 6, 7, 8 → 2 deuterium lineswhere p is the principle quantum. The temperature is determined by usingthe knowledge that the population densities of deuterium atoms with energylevels greater than p = 5 are in Saha equilibrium and therefore have the tem-perature dependent distribution ofnp ∝ p2T3/2eexp(13.6Tep2), (1)where np is the population density of electrons in level p and Te is the electrontemperature in eV.[8]The spectral data recorded by a visible spectrometer are line integrationsthrough different divertor regions. The temperature and density measure-ments can be spatially localized by recognizing that most of the line integratedbrightness comes from the region where the emission is greatest. Thus, the dis-tribution of the emission determines how well localized the measurement is.For brevity the chordal measured ne and Te have been attributed to the peakin the emission along the viewing chord. Terry, et al.,[9] discusses and definesthe number of recombinations per Dγ photon concept that is used here to de-termine the rate of volume recombination. The recombinations per Dγ photoncurves show a strong temperature dependence to Te for Te ≤ 0.8eV, but a lessthan linear dependence upon ne.Using the Dγ emission profile from Fig. (2), the temperature and densitymeasurements from the visible spectrometer, and the recombinations per Dγphoton curves, the recombinations per unit volume per unit time has beenmeasured and summed over the PFZ volume only. Therefore the total recom-binations in the PFZ are determined as a function of time. If we assume thatall of the plasma particles that enter the PFZ volumetrically recombine, wecan relate this measurement to the total plasma particle current into the PFZ.3 ObservationsAs the density is increased, four distinct Dγ profile distributions are observed.These are shown in Fig. (2). The first, Fig. (2a), occurs when the density is lowand the inner nose is completely detached. There is only Dγ emission on theinner nose, with no emission in the PFZ or along the outer leg. The second,Fig. (2b), is at a somewhat higher density and shows that the emission on theouter nose is decreased and a significant amount of emission comes from thePFZ, with still no emission in the CFZ of the outer leg. The third case, Fig.(2c), is the initially detached case where the outer leg CFZ has a small but30.45 0.55 0.65 0.75R (m)-0.60-0.47-0.33Z (m)0.55 0.65 0.7515kW m-3117.3.0.-0.60-0.47-0.33(a) (b)(c) (d)Fig. 2. Four Dγ emission profiles as the n¯e increases (a) n¯e = 1.16 × 1020 m−3,(b) n¯e = 1.66× 1020 m−3, (c) detachment starts, n¯e = 1.86× 1020 m−3, and, (d)expanded detachment front, n¯e = 2.30× 1020 m−3.intense region of emission located at the strikepoint, and the PFZ emissionhas decreased somewhat from Fig. (2b). In this case the inner nose emissionchanges very little when compared to Fig. (2b). The final case, Fig. (2d),shows a region of detachment extending along the outer divertor leg, All ofthe measured Dγ emission is on the outer leg extending to the x-point. Thered lines in Fig. (2) indicate the separatrix.4 Derivation of radial driftWe hypothesize that the flux of plasma into the PFZ is due to a drift generatedby a temperature gradient in the poloidal direction. This drift has been dis-cussed in previous articles[10–13] to explain the in/out asymmetry of tokamakdivertors. A brief derivation of the radial drift is given below.4From the momentum conservation equation from Braginskii[14],mened~vedt= −∇Pe − ene(~E + ~ve × ~B)+ ~R. (2)By neglecting the electron inertia term (me → 0) and assuming a scalar pres-sure, Eq. (2) is reduced to0 = −∇pe − ene(~E + ~ve × ~B)+ ~R, (3)where~R = −meneτe(0.51u||~ˆb+ ~u⊥)− 0.71ne~ˆb · ∇Te − 32neωeτe~ˆb×∇Te (4)is the momentum exchange term due to friction between the two speciesfor a hydrogenic plasma, ~ˆb is the unit vector parallel to the magnetic field,~u = ~ve − ~vi, ωe is the electron cyclotron frequency, and τe is the inverseelectron-ion collision frequency. Figure (3) shows the coordinate system usedfor this analysis. The s-direction is parallel to the magnetic field, w-direction isperpendicular to the magnetic field but on the flux surface, and the r-directionis normal to the magnetic flux surface. The toroidal component of Eqs. (3)and (4) with the assumption of toroidal symmetry (∂/∂φ = 0) is0 =−eneEφ + eneverBθ − meneτeuφ + 0.49meneτeBφBus−0.71neBφB∂Te∂s− 32BθBneωeτe∂Te∂r, (5)where φ represents the toroidal direction and θ represents the poloidal direc-tion. Solving Eq. (5) for ver yieldsver =EφBθ− mee2ne1τeBθJφ − 0.49 meeτeBθBφBus + 0.71BφB1eBθ∂Te∂s+321eB1ωeτe∂Te∂r, (6)where Jφ = −eneuφ. us and the temperature gradient can be reduced totoroidal and poloidal projections using toroidal symmetry and the assumptionthat there is no poloidal current in this region (uθ = 0). Therefore Eq. (6) canbe written as,ver =EφBθ+mee2ne1τeBθ[1 − 0.49α−1]Jφ + 0.71α−1 1eBφ∂Te∂θ5Bθ BφBrs wI,BφFig. 3. Coordinate system used in the derivation of the thermoelectric radial drift.+321eBφα−121ωeτe∂Te∂r, (7)where α =(1 +B2θ/B2φ). Since, α ≈ 1,ver ≈ EφBθ+ 0.51mee2ne1τeBθJφ + 0.711eBφ∂Te∂θ+321eBφ1ωeτe∂Te∂r. (8)A similar derivation can be done for the ions and yields the same result.Of the four terms in Eq. (8) the third term is dominant. The toroidal electricfield and current contributions should nearly cancel. For the fourth term tobe on the order of the third the radial temperature gradient must be ≈ 105times steeper than the poloidal temperature gradient. As will be seen, in thecases of interest it is typically only ten times higher. Therefore the radial driftis dominant and will be dealt with exclusively,ver ≈ 0.71 1eBφ∂Te∂θ. (9)This means that the existence of a poloidal temperature gradient on the outerleg from the X-point to the strikepoint leads to a radially inward drift ofplasma into the PFZ.65 Qualitative AnalysisThe agreement between the hypothesis that the drift is due to poloidal tem-perature gradient and the observations can be seen beginning with the firstcase, Fig. (2a), where the inner nose is detached and the outer nose is at-tached. The temperature gradient is shallow (50 → 25 eV) and the density islow enough along the outer leg create only a weak flux of particles (∼ 1020particles s−1)) entering the PFZ . With this weak flux of particles the densityin the PFZ cannot rise to the level required for volumetric recombination to beevident by strong Dγ emission, and no Dγ emission is seen. In the second case,Fig. (2b), can be described as high-recycling; pressure is constant on a fluxsurface but, not poloidal density and temperature. Therefore there should beplasma in the PFZ, and it is observed. The third case, Fig. (2c), is the partiallydetached case. Here the pressure is not constant, but modeling shows that thegradients still exist below the x-point to the detachment front.[15] In such acase, it is expected that the plasma will flow into the PFZ only above thissharp gradient region and not below it. This is what is observed in Fig. (2c).In last case, Fig. (2d), the region of sharp temperature gradient has moved allthe way to the x-point. There is only a shallow gradient along the outer leg.This yields no flow from the outer leg into the PFZ. Instead, in this case thepoloidal gradient will drive a flow into the core directly above the x-point. Asthe density increases, the flux into the core above the x-point increases, and acold MARFE forms above the x-point eventually leading to a disruption. Thisis seen on Alcator C-Mod.[6,7]The distribution of the Dγ emission does not agree with the possibility ofperpendicular diffusion being the dominant mechanism fueling the PFZ. Ifdiffusion was the main cause of particle flux into the PFZ one would expectthe particle flux to increase when the divertor detachment is extended to thex-point due to the large perpendicular density gradient formed on the outerleg. This is not observed and therefore cross-field diffusion is not consideredto be the dominant mechanism.6 Quantitative AnalysisThe total number of particles per second that drift into the private flux regionisIe =∫never dA, (10)7where∫. . . dA is the integral over the total area of the outer leg. By substi-tuting Eq. (9) into Eq. (10) and recognizing that in a tokamak Bφ = BoRo/R,where Bo and Ro are the magnetic field and radial position of the center ofthe main plasma, the particle current into the PFZ can be written asIe ≈ 1.42pieBoRox∫spneR2∂Te∂θdθ, (11)where sp is the strikepoint, x is the x-point. In the attached case (∂pe/∂s = 0)this integral can be approximated as,Ie ≈ 1.42piR2peeBoRoln(TxTsp)(12)assuming the variation in R2 is small enough to remove it from inside theintegral.Using the assumption that all plasma particles that enter the PFZ volu-metrically recombine in the PFZ and using the approximations that yieldedEq. (12), the relation between the PFZ recombination rate and the particlecurrent into the PFZ is(∂Ne∂t)recomb≈ βpe, (13)whereβ =1.42piR2eBoRoln(TxTsp). (14)Figure (4) shows the comparison of the PFZ recombination rate as a functionof peak plasma pressure on the outer leg for the discharge shown in Fig. (2).The linear dependence is what is expected from Eq. (13).The line shown in Fig. (4) is a linear regression fit of the data. This yields aslope of 6.3 × 1018 recombinations s−1 Pa−1 with an R2 value of 0.826. Giventhat R ≈ 0.6m, Bo = 5.4T, and Ro = 0.67m and if ln(Tx/Tsp)≈ 2.25 then,the slope is the same as predicted from Eq. (14).80.0 0.5 1.0 1.5 2.0Pressure (kPa)0246810Recombination Rate (1021 s-1 )Fig. 4. A plot of the PFZ recombination rate as a function of the peak electronpressure on the outer leg when the outer leg was attached for the shot in Fig. (2).7 Discussion and SummaryDγ emission shows the existence of plasma in the private flux zone of theAlcator C-Mod tokamak. Using spectroscopic measurement we observe thatthere is a significant recombination rate in this region, which is likely fed bycross-field transport from across the separatrix. From Braginskii’s equations, aradial drift is derived to explain the behavior of the PFZ plasma. The dominantdrift is due to a poloidal temperature gradient. This mechanism for the fluxinto the PFZ is consistent with the observed behavior of the plasma.In the attached case the flux into the PFZ is linear with the plasma pressureand logarithmic with respect to the ratio of x-point temperature to temper-ature at the divertor plate. This linear behavior is observed and verified onAlcator C-Mod.As the line averaged density is increased the outer divertor leg becomes de-tached and a sharp poloidal temperature gradient is located at or slightlyabove the x-point, thus reducing the flow into the PFZ. As the density is in-creased further plasma flows into the x-point from the CFZ due to the localtemperature gradient. This cools the plasma on the closed flux surfaces enoughto generate an x-point MARFE, which subsequently leads to disruption. Thishas been observed on the Alcator C-Mod tokamak.[6,7]98 AcknowledgementsThe authors would like to thank the Alcator C-Mod group for assistance inacquiring these data. The authors would also like to extend there gratitudeto Prof. P. C. Stangeby for his helpful discussions on the topic of the ~E × ~Bdrift. This work was supported by the U. S. Dept. of Energy under grant#DE-FC02-99ER54512.References[1] I. H. Hutchinson et al., Physics of Plasmas 1, 1511 (1994).[2] B. LaBombard et al., Journal of Nuclear Materials 220–222, 976 (1995).[3] G. M. McCracken et al., Nuclear Fusion 38, 619 (1998).[4] G. M. McCracken et al., Journal of Nuclear Materials 266–269, 37 (1999).[5] M. E. Fenstermacher et al., Journal of Nuclear Materials 266–269, 348 (1999).[6] B. Lipschultz et al., Journal of Nuclear Materials 266–269, 370 (1999).[7] B. Lipschultz et al., Physics of Plasmas 6, 1907 (1999).[8] B. Lipschultz et al., Physical Review Letters 81, 1007 (1998).[9] J. L. Terry et al., Physics of Plasmas 5, 1759 (1998).[10] F. L. Hinton and G. M. Staebler, Nuclear Fusion 29, 405 (1989).[11] G. M. Staebler, Nuclear Fusion 31, 729 (1991).[12] A. V. Chankin et al., Plasma Phys. Control. Fusion 36, 1853 (1994).[13] P. C. Stangeby and A. V. Chankin, Nuclear Fusion 36, 839 (1996).[14] S. I. Braginskii, Reviews of Plasma Physics (Consultants Bureau, New York,1965), Vol. 1.[15] F. Wising et al., Contributions to Plasma Physics 36, 136 (1996).10

Observations of Cold, High Density Plasma in the Private Flux Region of the Alcator C-Mod Divertor

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Observations of Cold, High Density Plasma in the Private Flux Region of the Alcator C-Mod Divertor

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